Discrete Applied Mathematics Seminar by Dheer Desai: Spectral Turan Problems on trees and even cycles
Speaker: , University of Wyoming
Title: Spectral Tur谩n Problems on Trees and Even Cycles
Abstract: In this talk, we discuss some recent progress with the spectral analogue of a few Tur谩n problems: Instead of maximizing the number of edges, our objective is to maximize the spectral radius of the adjacency matrices of graphs not containing some forbidden subgraph(s).
We will overview some known results and compare extremal graphs for both kinds of problems. A celebrated theorem of Erd枚s, Stone and Simonovits gives the asymptotics of the Tur谩n numbers for forbidden graphs with chromatic number more than 2. A similar result also holds for the spectral Tur谩n numbers. In contrast, the asymptotics are not known for several basic bipartite graphs.
We will discuss a recursive method that was initially used to obtain spectral Tur谩n results when the forbidden graphs had chromatic number more than two, and has recently been used to find spectral extremal graphs for even cycles and trees.
Please contact the seminar organizers, Samantha Dahlberg (sdahlberg@iit.edu) and Hemanshu Kaul (kaul@iitt.edu), for online joining info.
Discrete Applied Math Seminar
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